As for fake resume studies, the problem with those is that male and female resumes are evaluated differently. If they made a male looking resume and sent it out with a female name it will do badly. But a female looking resume with a male name will also do badly.
The prime example is the term "bossy", women get called this since they are expected to be much more cooperative than men. I think a very big issue right now is that we use men as a standard and say "when women use male strategies they get pushback for being too masculine", instead to gain individual success they should try to be like successful women. In an ideal society this wouldn't be the case, but as is these biases exists and so you have to work with them.
And as a personal anecdote, when I looked for jobs as a new grad when I used more cooperative and less personal excellence I didn't get any callbacks. I got lots of callbacks when I focused on personal excellence though. Its as if companies assumed I was less competent just because I talk about teamwork, because their ideal masculine software engineer wouldn't talk like that. You can see here how it works:
https://hbr.org/2018/10/how-men-get-penalized-for-straying-f...
Edit: The moral of the story is that when we tell men to be more feminine and women to be more masculine we just hurt them. Men and women aren't evaluated by the same metrics. People told me "Companies expects you to be a teamplayer, try to highlight that!", but it was clearly wrong and didn't help me at all.
The whole idea that there's a competency bias towards men is false. What's actually being observed is that women are hired even when they aren't competent, to please feminists and diversity advocates, which then by definition would make men "appear" more competent even if they were of only average competency.